Level-0 Models for Predicting Human Behavior in Games

Abstract

Behavioral game theory seeks to describe the way actual people (as compared to idealized, "rational" agents) act in strategic situations. Our own recent work has identified iterative models, such as quantal cognitive hierarchy, as the state of the art for predicting human play in unrepeated, simultaneous-move games. Iterative models predict that agents reason iteratively about their opponents, building up from a specification of nonstrategic behavior called level-0. A modeler is in principle free to choose any description of level-0 behavior that makes sense for a given setting. However, in practice almost all existing work specifies this behavior as a uniform distribution over actions. In most games it is not plausible that even nonstrategic agents would choose an action uniformly at random, nor that other agents would expect them to do so. A more accurate model for level-0 behavior has the potential to dramatically improve predictions of human behavior, since a substantial fraction of agents may play level-0 strategies directly, and furthermore since iterative models ground all higher-level strategies in responses to the level-0 strategy. Our work considers models of the way in which level-0 agents construct a probability distribution over actions, given an arbitrary game. We considered a large space of alternatives and, in the end, recommend a model that achieved excellent performance across the board: a linear weighting of four binary features, each of which is general in the sense that it can be computed from any normal form game. Adding real-valued variants of the same four features yielded further improvements in performance, albeit with a corresponding increase in the number of parameters needing to be estimated. We evaluated the effects of combining these new level-0 models with several iterative models and observed large improvements in predictive accuracy.